Authors: | Horiuchi, Kiyomitsu Šešelja, Branimir Tepavčević, Andreja |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Trice-valued fuzzy sets: Mathematical model for three-way decisions | Journal: | Information Sciences | Volume: | 507 | First page: | 574 | Last page: | 584 | Issue Date: | 1-Jan-2020 | Rank: | M21a | ISSN: | 0020-0255 | DOI: | 10.1016/j.ins.2018.09.007 | Abstract: | Under the idea to develop a mathematical model for three-way decisions, the aim of the paper is to study trice-valued fuzzy sets, i.e., mappings from a set to a structure called a trice. A trice is a triple semilattice satisfying roundabout absorption laws, suitable for representing multi-dimensional orders, which appear in complex movements in a plane or in a space. Our approach is cutworthy, namely, we investigate cuts of such fuzzy sets and prove theorems of decomposition and synthesis. This new notion provides a possibility to capture vague triangular situations. Therefore, a motivation for our research is to provide a new algebraic and order-theoretic model for three-way decisions, as this topic has been introduced recently for solving particular human problems and for information processing. |
Keywords: | Cuts | Shadowed sets | Three-way decisions | Trice | Trice-valued fuzzy sets | Triple semilattice | Publisher: | Elsevier | Project: | Development of methods of computation and information processing: theory and applications Provincial Secretariat for Higher Education and Scientific Research, Grant no. 142-451-3642/2017/01 |
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